Pellegrini left La Liga to take over at the Etihad Stadium this summer, after Roberto Mancini was sacked, and has promised to improve City's brand of football.
The Chilean guided Malaga to the quarter-finals of the Champions League last season and Milner says Pellegrini is keen to replicate the same defensive tactics with City that he used to such great effect in Spain.
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"It will take a bit of time to get everyone on the same page as to how he wants us to play and get that, but once it clicks - I think you can see the jobs he has done at his previous clubs.
"We have watched videos of his previous teams doing it to get prepared and see exactly how he wants things doing, as well as doing it on the training field.
"You see the organisation and the record Malaga had in the Champions League last year was really good defensively."
City are currently in Hong Kong for the Barclays Asia Trophy, along with fellow Premier League sides Tottenham and Sunderland, but Pellegrini has had to leave the pre-season tour due to the death of his mother.
Assistant managers Brian Kidd and Ruben Cousillas Fuse have taken over in the manager’s absence, and Milner says the players are focussed on their football.
"Obviously the manager is new anyway, he is still getting to grips," Milner added.
"Ruben and Kiddo took over. We are used to changes and things like that, so we just get on with the job in hand.
"Hopefully everything is all right with the manager."